Oh, just for information's sake for people unfamiliar with the game/anime, I just realized that GameFAQs has an entire transcription of the game included. Here is the relevant section where Vyers/Mid-Boss is introduced:
--- IV.ii.d. Hall of Caresses ---
[Camera shows a magnificent room within Vyers Castle, highlighted by a red couch in the center]Laharl: Hm? Is this the last room?
Voice: Haaahahahaha!!
Laharl: Who's there!?
Voice: How rude, invading a man's house and asking him, "Who's there?"
Voice: But, I give you credit for your bravery.
Voice: Haaaaaaahhhh!!
Sassy Demon: Voila!
Sassy Demon: ...Forgive moi, I must leave you in awe.
Sassy Demon: My name is Vyers. I am the lord of this castle.
Etna: Vyers? Isn't he the demon that's been knocking off competition for the throne...?
Vyers: Oui. That is correct, mademoiselle.
Vyers: I am an aristocrat with both strength and beauty... They call moi the "Dark Adonis".
Vyers: ...Young man. I assume that you are the son of the late King Krichevskoy, are you not?
Laharl: That's right. I'm Laharl, the heir to the throne.
Vyers: The heir to the throne?
Vyers: Hah! That is history, dear boy. Your existence has long been forgotten...
Vyers: Are you blind to the horde of demons lining up to fight for the throne?
Laharl: So? I'm the heir. That's all that matters.
Laharl: If they've forgotten, then I'll just have to make them remember.
Vyers: I see. So you saw my potential and decided to strike first against moi...
Vyers: Such wonderful intuition... Well played, son of Krichevskoy.
Laharl: I've never even heard of you. It's only a coincidence that we're here.
Laharl: You're just a tiny stepping stone on my path to the throne.
Vyers: *gasp* How dare you! I am the Dark Adonis Vy...
Laharl: Who gives a damn about you? Your new name is "Mid-Boss".
Vyers: Mi, Mi, Mid-Boss!?
Etna: Looks like you hurt his pride, Prince.
Mid-Boss: Unforgivable...
Mid-Boss: That is unforgivable!!!![Fade to black]
This also happens to be the last place Vyers' actual name is used, he is cut off every time henceforth he tries to use it. So I'm not sure who's case that helps more, but it does clearly establish Vyers' name via self-introduction within the canon storyline. It also shows that his real name not being used is not complicit like it is in Osaka's case where we still don't use her established and accepted nickname.
Updated by Shinjidude